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November 1, 2021 03:35Subject:

Re: how do I turn a real into and array of Integers?Message ID:

2b36075c-8232-3ee3-19b9-3c363c20f7e2@zoho.comOn 10/31/21 19:39, Sean McAfee wrote: > On Sun, Oct 31, 2021 at 6:51 PM ToddAndMargo via perl6-users > <perl6-users@perl.org <mailto:perl6-users@perl.org>> wrote: > > >> How do I get more digits out of sqrt? > > On 10/31/21 17:50, Kevin Pye wrote: > > You don't. > > > > sqrt is a function which acts on 64-bit floating point numbers, and > there's no more meaningful digits available. If you need more precision > you're on your own. > > Dang! I was hoping ther was some thing like UInt. > > > Fortunately, it's easy. > > Wikipedia describes the following recurrence formula for approximating > the square root of 2 from an initial guess a₀: > > aₙ₊₁ = (aₙ / 2 + 1 / aₙ) > > So just iterate this sequence until successive terms become close enough > for you, using the unlimited precision FatRat type, for example: > > (2.FatRat, { $_ / 2 + 1 / $_ } ... (* - *).abs < 1e-100).tail > > This gives the root to a precision of one in a googol. > > (2.FatRat, { $_ / 2 + 1 / $_ } ... (* - *).abs < 1e-100).tail 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497099935831413222665927505592755799950501152782060571 Awesome!Thread Previous | Thread Next

- how do I turn a real into and array of Integers? by ToddAndMargo via perl6-users
- Re: how do I turn a real into and array of Integers? by Andinus via perl6-users
- Re: how do I turn a real into and array of Integers? by Sean McAfee
- Re: how do I turn a real into and array of Integers? by ToddAndMargo via perl6-users
- Re: how do I turn a real into and array of Integers? by ToddAndMargo via perl6-users
- Re: how do I turn a real into and array of Integers? by Kevin Pye
- Re: how do I turn a real into and array of Integers? by ToddAndMargo via perl6-users
- Re: how do I turn a real into and array of Integers? by Sean McAfee
**Re: how do I turn a real into and array of Integers?**by ToddAndMargo via perl6-users- Re: how do I turn a real into and array of Integers? by sisyphus
- Re: how do I turn a real into and array of Integers? by Sean McAfee
- Re: how do I turn a real into and array of Integers? by Alice
- Re: how do I turn a real into and array of Integers? by Shlomi Fish
- Re: how do I turn a real into and array of Integers? by ToddAndMargo via perl6-users
- Re: how do I turn a real into and array of Integers? by Bruce Gray
- Re: how do I turn a real into and array of Integers? by sisyphus
- Re: how do I turn a real into and array of Integers? by William Michels via perl6-users
- Re: how do I turn a real into and array of Integers? by Patrick R. Michaud
- Re: how do I turn a real into and array of Integers? by William Michels via perl6-users
- Re: how do I turn a real into and array of Integers? by ToddAndMargo via perl6-users

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